A flexible temporal velocity model for fast contaminant transport simulations in porous media

In subsurface aquifers, dispersion of contaminants is highly affected by the heterogeneity of the hydraulic conductivity field. As an alternative to Monte Carlo simulations on probable conductivity fields, stochastic velocity processes have been introduced to assess the uncertainty in the transport of contaminants. In continuum-scale simulations, discrete velocity models (such as correlated continuous time random walk) focus on modeling plume dispersion in the longitudinal direction. There are alternative continuous velocity processes (such as the polar Markovian velocity process [PMVP]) that are able to accurately model transport in both longitudinal and transverse directions. Importantly, the PMVP model correctly predicts the limited spreading of the ensemble contaminant plume in the transverse direction. However, the stochastic differential equations used in the PMVP model have specific drift and diffusion functions that are designed for the exponential correlation structure. In this paper, a new discrete velocity process is described that is applicable to modeling transport in two-dimensional conductivity fields for both Gaussian and exponential correlation structures. This method is simple, in a sense that it does not require modeling the functional form of the drift and diffusion functions. The new method is validated against Monte Carlo simulations for both correlation structures with high variances of log conductivity.